Question: $a_n=\dfrac{3^{2n+1}}{9^n\sqrt{n}}$ 1) Find $\lim_{n\to\infty}\left| \dfrac{a_{n+1}}{a_n} \right|$. $\lim_{n\to\infty}\left|\, \frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=$
Answer: $\lim_{n\to\infty}\left| \,\frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=1$ Since the limit is equal to $1$, the ratio test is inconclusive.